I've googled for a formula to equate the probability of a horse running 2nd or 3rd but the mathematical models requires a phD in mathematics to understand!
Anyone ever come across anything that can predict probability % of a 2nd or 3rd placing based on Actual results?
RP

Attached is an image from Berkley University. What do you think? Maybe someone like Eva can fathom what's going ON!!

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That one is a little above me, RP.
However, from working the Betfair place markets and general observations of place dividend differences compared with win odds, I don't think there can be a direct formula that is accurate.

The bookies use 1/5th the win odds for the place on most races, but to work out the chances of running second or third is something else. It does not just depend on the win odds, but also on the horse's statistics or individual chances of running second or third based on strike rate, class, win odds, etc etc.

Even the bookies 1/5th is flawed because a horse's place chance cannot be directly derived from the win price. This is why many bookies will only bet win only, others each way only, but usually place betting is only available where the bookie has built in a massive overround to cover the anomalies that can be exploited by the savvy.

In fact, this is one area that will cause a closing of account from online corporates. If they suspect one is exploiting anomalies regardless of odds, then the account is flagged immediately.

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Not sure but I've googled some more and will have a crack at a a highly simplified solution for Horse 1 running 2nd...

5 horse race for simplification:
=> % winning chance(and probability out of 1) for each
1 20% = 0.20
2 20% = 0.20
3 30% = 0.30
4 15% = 0.15
5 15% = 0.15
TOTAL 100% = 1.00

Horse 1 can come 2nd in the following ways... 2-1,3-1,4-1,5-1
So taking each, 1 at a time...
=>2-1: P=0.20 x 0.20/0.80 = 0.05

(because total probability available for 2nd place getter is reduced by 0.20 given that first place has already happened i.e. 1.0-0.20=0.80)

=>3-1: P = 0.30x0.20/0.70 = 0.0857
=>4-1: P = 0.15 x 0.20/0.85 = 0.0353
=>5-1: P = same = 0.0353

Therefore, probability of Horse 1 running second to 2 OR 3 OR 4 OR 5 ;

P(1 runs 2nd) = 0.05 + 0.0857 + 0.0353 + 0.0353 = 0.2063 = 20.6%


Perhaps one of the maths freaks on here can verify the above and compute the equivalent for Horse 1 running 3rd.

If my maths is correct, probability of Horse 1 running 2nd OR 3rd is;

=> P(1 runs 2nd or 3rd) = 0.2063 + P (1 runs 3rd)


Cheers LG

PS would be easier using XL for standard sized field but just an illustration here and frankly.. I can't be jacked whipping up one tonight. Enjoy!

PSS Note Chrome's comment above("It does not just depend on the win odds...") and hence my highly simplified solution!!

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The trick isn't finding profitable angles, it's finding ones you will bet through the ups and downs - UB

The chances of a horse placing is dependant on the price of the fav and the price of the horse. Currently a work in progress.
Consider 4th rank.
All in 81200 races win % 10.1% Place % 33.2%. Remembering that 10% wins included so the all in 2nd and 3rd place SR is only 23.1%. With the Fav price from $1 up to $4.50 the place SR goes from 27.5% up to 35.4% while the win SR goes from 6.3% up to 12%. I have only got a quarter way through and only doing it in 50 cent increments.

Here is an interesting alternative and me attempting to apply some outside of the box thinking a la Ricon de Paul

Assume that the chance of Horse 1 winning is 10.1%, 2nd place is now effectively the winner of a race home containing the rest of the field, the total probability available now for the remaining runners being 100 - 10.1 = 89.9%

Whilst I appreciate that we are not talking independent events here, this model is one of many races happening simultaneously with decreasing field size, which is effectively what is happening. The total probability remains the same however = 1.00 or 100%

Just my deluded thoughts. Not enough funny water here to make them logical!

LG

__________________
The trick isn't finding profitable angles, it's finding ones you will bet through the ups and downs - UB

One more insight on this and then I'm off for a kip..

It comes from the same Berkeley article you alude to in Post 1, RP(did you even read 4. Concluding Remarks OR just look at the pics ?!)

All models suffer from favorite - longshot bias i.e. the probability of finishing second or third is overestimated for horses which have a high probability of winning and underestimated for those which have a low probability of winning.

Kind of makes sense when you think about it, or maybe it doesn't?

Good night.

LG

__________________
The trick isn't finding profitable angles, it's finding ones you will bet through the ups and downs - UB

I can work out the true odds of a horse running 2nd or 3rd for various prices and field sizes using statistics, and this will be accurate over thousands of races, BUT it will not be accurate for each single event.

In other words, one could not use this for overlay betting as each single event should have different odds of happening due to extra factors. This is why 1/5th the odds for placing first, second or third is not good for bookmakers because of savvy punters taking advantage of the calculated overlays for each event.

Hope this makes sense.

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Here's an example for $2.00 SP Favourites:

Starters Win Chance Place Chance 2nd Chance 3rd Chance

   3      45.37%       100%       31.48%     22.22%

   4      45.48%       88.25%     28.92%     14.16%

   5      41.69%       85.09%     28.50%     15.04%

   6      40.17%       82.20%     26.65%     15.38%

   7      40.56%       79.35%     24.37%     14.41%

   8      40.72%       77.08%     23.22%     13.15%

   9      40.26%       74.74%     19.98%     14.49%

etc. etc.

You can see why there is no place betting on four runners or less, and why there is no third dividend on 7 runners or less.

1/5th the odds from the bookie for the place, means you lose $7.50 for every hundred bets on 8 runners, $10.31 for every hundred bets on 9 runners etc etc. The larger the field the more the odds are in favour of the bookie.

However, this is carte blanche, there are many instances where an individual horse has a better place chance than the 1/5th offered.
That is why you lose money if betting everything, but make money backing champions.

__________________
RaceCensus - powerful system testing software.
Now with over 407,000 Metropolitan, Provincial and Country races!
http://www.propun.com.au/horse_raci...ng_systems.html
*RaceCensus now updated to 30/09/2024
Video overview of RaceCensus here:
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Overwhelmed by your responses, thanks heaps.
The reason behind my interest, is I've been running the bot for the past week on a Lay the Place ~ Aus markets, an old system of Bhag's from 2011. It's been a little beauty, although not so good on the UK races.
I've never taken much notice of the BF Place market for Laying before, due to the low turnovers.
Bhag's scheme works the underlays it seems, but determining what's an under/overlay in the Place market is the conundrum? For the longshot layers there would appear to be good value in this market from the point of view of achieving your 10% of Bank quickly, if that's your target given you might be a "Seven Squared on Speed" follower. (hint, hint...Speedy)

I think Beton & CP's tact of basing stats on past performances rather than some mathematical formula is the safest bet?
Cheers, and remember, Have a Great Day! RP